TSTP Solution File: NUM519+3 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : NUM519+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 10:19:21 EDT 2022
% Result : Theorem 34.79s 22.23s
% Output : Proof 34.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM519+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : goeland -dmt -presko -proof %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 11:22:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 [DMT] DMT loaded with preskolemization
% 0.12/0.34 [EQ] equality loaded.
% 0.12/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.12/0.36 Start search
% 0.12/0.36 nb_step : 1 - limit : 70
% 0.12/0.36 Launch Gotab with destructive = true
% 34.79/22.21 % SZS output start Proof for theBenchmark.p
% 34.79/22.23 [0] ALPHA_AND : (! [W05_5] : ((aNaturalNumber0(W05_5) => $true)) & aNaturalNumber0(sz00) & (aNaturalNumber0(sz10) & ~=(sz10, sz00)) & ! [W06_6, W17_7] : (((aNaturalNumber0(W06_6) & aNaturalNumber0(W17_7)) => aNaturalNumber0(sdtpldt0(W06_6, W17_7)))) & ! [W08_8, W19_9] : (((aNaturalNumber0(W08_8) & aNaturalNumber0(W19_9)) => aNaturalNumber0(sdtasdt0(W08_8, W19_9)))) & ! [W010_10, W111_11] : (((aNaturalNumber0(W010_10) & aNaturalNumber0(W111_11)) => =(sdtpldt0(W010_10, W111_11), sdtpldt0(W111_11, W010_10)))) & ! [W012_12, W113_13, W214_14] : ((((aNaturalNumber0(W012_12) & aNaturalNumber0(W113_13)) & aNaturalNumber0(W214_14)) => =(sdtpldt0(sdtpldt0(W012_12, W113_13), W214_14), sdtpldt0(W012_12, sdtpldt0(W113_13, W214_14))))) & ! [W015_15] : ((aNaturalNumber0(W015_15) => (=(sdtpldt0(W015_15, sz00), W015_15) & =(W015_15, sdtpldt0(sz00, W015_15))))) & ! [W016_16, W117_17] : (((aNaturalNumber0(W016_16) & aNaturalNumber0(W117_17)) => =(sdtasdt0(W016_16, W117_17), sdtasdt0(W117_17, W016_16)))) & ! [W018_18, W119_19, W220_20] : ((((aNaturalNumber0(W018_18) & aNaturalNumber0(W119_19)) & aNaturalNumber0(W220_20)) => =(sdtasdt0(sdtasdt0(W018_18, W119_19), W220_20), sdtasdt0(W018_18, sdtasdt0(W119_19, W220_20))))) & ! [W021_21] : ((aNaturalNumber0(W021_21) => (=(sdtasdt0(W021_21, sz10), W021_21) & =(W021_21, sdtasdt0(sz10, W021_21))))) & ! [W022_22] : ((aNaturalNumber0(W022_22) => (=(sdtasdt0(W022_22, sz00), sz00) & =(sz00, sdtasdt0(sz00, W022_22))))) & ! [W023_23, W124_24, W225_25] : ((((aNaturalNumber0(W023_23) & aNaturalNumber0(W124_24)) & aNaturalNumber0(W225_25)) => (=(sdtasdt0(W023_23, sdtpldt0(W124_24, W225_25)), sdtpldt0(sdtasdt0(W023_23, W124_24), sdtasdt0(W023_23, W225_25))) & =(sdtasdt0(sdtpldt0(W124_24, W225_25), W023_23), sdtpldt0(sdtasdt0(W124_24, W023_23), sdtasdt0(W225_25, W023_23)))))) & ! [W026_26, W127_27, W228_28] : ((((aNaturalNumber0(W026_26) & aNaturalNumber0(W127_27)) & aNaturalNumber0(W228_28)) => ((=(sdtpldt0(W026_26, W127_27), sdtpldt0(W026_26, W228_28)) | =(sdtpldt0(W127_27, W026_26), sdtpldt0(W228_28, W026_26))) => =(W127_27, W228_28)))) & ! [W029_29] : ((aNaturalNumber0(W029_29) => (~=(W029_29, sz00) => ! [W130_30, W231_31] : (((aNaturalNumber0(W130_30) & aNaturalNumber0(W231_31)) => ((=(sdtasdt0(W029_29, W130_30), sdtasdt0(W029_29, W231_31)) | =(sdtasdt0(W130_30, W029_29), sdtasdt0(W231_31, W029_29))) => =(W130_30, W231_31))))))) & ! [W032_32, W133_33] : (((aNaturalNumber0(W032_32) & aNaturalNumber0(W133_33)) => (=(sdtpldt0(W032_32, W133_33), sz00) => (=(W032_32, sz00) & =(W133_33, sz00))))) & ! [W034_34, W135_35] : (((aNaturalNumber0(W034_34) & aNaturalNumber0(W135_35)) => (=(sdtasdt0(W034_34, W135_35), sz00) => (=(W034_34, sz00) | =(W135_35, sz00))))) & ! [W036_36, W137_37] : (((aNaturalNumber0(W036_36) & aNaturalNumber0(W137_37)) => (sdtlseqdt0(W036_36, W137_37) <=> ? [W238_38] : ((aNaturalNumber0(W238_38) & =(sdtpldt0(W036_36, W238_38), W137_37)))))) & ! [W039_39, W140_40] : (((aNaturalNumber0(W039_39) & aNaturalNumber0(W140_40)) => (sdtlseqdt0(W039_39, W140_40) => ! [W241_41] : ((=(W241_41, sdtmndt0(W140_40, W039_39)) <=> (aNaturalNumber0(W241_41) & =(sdtpldt0(W039_39, W241_41), W140_40))))))) & ! [W042_42] : ((aNaturalNumber0(W042_42) => sdtlseqdt0(W042_42, W042_42))) & ! [W043_43, W144_44] : (((aNaturalNumber0(W043_43) & aNaturalNumber0(W144_44)) => ((sdtlseqdt0(W043_43, W144_44) & sdtlseqdt0(W144_44, W043_43)) => =(W043_43, W144_44)))) & ! [W045_45, W146_46, W247_47] : ((((aNaturalNumber0(W045_45) & aNaturalNumber0(W146_46)) & aNaturalNumber0(W247_47)) => ((sdtlseqdt0(W045_45, W146_46) & sdtlseqdt0(W146_46, W247_47)) => sdtlseqdt0(W045_45, W247_47)))) & ! [W048_48, W149_49] : (((aNaturalNumber0(W048_48) & aNaturalNumber0(W149_49)) => (sdtlseqdt0(W048_48, W149_49) | (~=(W149_49, W048_48) & sdtlseqdt0(W149_49, W048_48))))) & ! [W050_50, W151_51] : (((aNaturalNumber0(W050_50) & aNaturalNumber0(W151_51)) => ((~=(W050_50, W151_51) & sdtlseqdt0(W050_50, W151_51)) => ! [W252_52] : ((aNaturalNumber0(W252_52) => (((~=(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51)) & sdtlseqdt0(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51))) & ~=(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52))) & sdtlseqdt0(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52)))))))) & ! [W053_53, W154_54, W255_55] : ((((aNaturalNumber0(W053_53) & aNaturalNumber0(W154_54)) & aNaturalNumber0(W255_55)) => (((~=(W053_53, sz00) & ~=(W154_54, W255_55)) & sdtlseqdt0(W154_54, W255_55)) => (((~=(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55)) & sdtlseqdt0(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55))) & ~=(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53))) & sdtlseqdt0(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53)))))) & ! [W056_56] : ((aNaturalNumber0(W056_56) => ((=(W056_56, sz00) | =(W056_56, sz10)) | (~=(sz10, W056_56) & sdtlseqdt0(sz10, W056_56))))) & ! [W057_57, W158_58] : (((aNaturalNumber0(W057_57) & aNaturalNumber0(W158_58)) => (~=(W057_57, sz00) => sdtlseqdt0(W158_58, sdtasdt0(W158_58, W057_57))))) & ! [W059_59, W160_60] : (((aNaturalNumber0(W059_59) & aNaturalNumber0(W160_60)) => (iLess0(W059_59, W160_60) => $true))) & ! [W061_61, W162_62] : (((aNaturalNumber0(W061_61) & aNaturalNumber0(W162_62)) => ((~=(W061_61, W162_62) & sdtlseqdt0(W061_61, W162_62)) => iLess0(W061_61, W162_62)))) & ! [W063_63, W164_64] : (((aNaturalNumber0(W063_63) & aNaturalNumber0(W164_64)) => (doDivides0(W063_63, W164_64) <=> ? [W265_65] : ((aNaturalNumber0(W265_65) & =(W164_64, sdtasdt0(W063_63, W265_65))))))) & ! [W066_66, W167_67] : (((aNaturalNumber0(W066_66) & aNaturalNumber0(W167_67)) => ((~=(W066_66, sz00) & doDivides0(W066_66, W167_67)) => ! [W268_68] : ((=(W268_68, sdtsldt0(W167_67, W066_66)) <=> (aNaturalNumber0(W268_68) & =(W167_67, sdtasdt0(W066_66, W268_68)))))))) & ! [W069_69, W170_70, W271_71] : ((((aNaturalNumber0(W069_69) & aNaturalNumber0(W170_70)) & aNaturalNumber0(W271_71)) => ((doDivides0(W069_69, W170_70) & doDivides0(W170_70, W271_71)) => doDivides0(W069_69, W271_71)))) & ! [W072_72, W173_73, W274_74] : ((((aNaturalNumber0(W072_72) & aNaturalNumber0(W173_73)) & aNaturalNumber0(W274_74)) => ((doDivides0(W072_72, W173_73) & doDivides0(W072_72, W274_74)) => doDivides0(W072_72, sdtpldt0(W173_73, W274_74))))) & ! [W075_75, W176_76, W277_77] : ((((aNaturalNumber0(W075_75) & aNaturalNumber0(W176_76)) & aNaturalNumber0(W277_77)) => ((doDivides0(W075_75, W176_76) & doDivides0(W075_75, sdtpldt0(W176_76, W277_77))) => doDivides0(W075_75, W277_77)))) & ! [W078_78, W179_79] : (((aNaturalNumber0(W078_78) & aNaturalNumber0(W179_79)) => ((doDivides0(W078_78, W179_79) & ~=(W179_79, sz00)) => sdtlseqdt0(W078_78, W179_79)))) & ! [W080_80, W181_81] : (((aNaturalNumber0(W080_80) & aNaturalNumber0(W181_81)) => ((~=(W080_80, sz00) & doDivides0(W080_80, W181_81)) => ! [W282_82] : ((aNaturalNumber0(W282_82) => =(sdtasdt0(W282_82, sdtsldt0(W181_81, W080_80)), sdtsldt0(sdtasdt0(W282_82, W181_81), W080_80))))))) & ! [W083_83] : ((aNaturalNumber0(W083_83) => (isPrime0(W083_83) <=> ((~=(W083_83, sz00) & ~=(W083_83, sz10)) & ! [W184_84] : (((aNaturalNumber0(W184_84) & doDivides0(W184_84, W083_83)) => (=(W184_84, sz10) | =(W184_84, W083_83)))))))) & ! [W085_85] : ((((aNaturalNumber0(W085_85) & ~=(W085_85, sz00)) & ~=(W085_85, sz10)) => ? [W186_86] : (((aNaturalNumber0(W186_86) & doDivides0(W186_86, W085_85)) & isPrime0(W186_86))))) & ((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & ! [W087_87, W188_88, W289_89] : ((((aNaturalNumber0(W087_87) & aNaturalNumber0(W188_88)) & aNaturalNumber0(W289_89)) => (((((~=(W289_89, sz00) & ~=(W289_89, sz10)) & ! [W390_90] : ((((aNaturalNumber0(W390_90) & ? [W491_91] : ((aNaturalNumber0(W491_91) & =(W289_89, sdtasdt0(W390_90, W491_91))))) & doDivides0(W390_90, W289_89)) => (=(W390_90, sz10) | =(W390_90, W289_89))))) | isPrime0(W289_89)) & (? [W392_92] : ((aNaturalNumber0(W392_92) & =(sdtasdt0(W087_87, W188_88), sdtasdt0(W289_89, W392_92)))) | doDivides0(W289_89, sdtasdt0(W087_87, W188_88)))) => (iLess0(sdtpldt0(sdtpldt0(W087_87, W188_88), W289_89), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((? [W393_93] : ((aNaturalNumber0(W393_93) & =(W087_87, sdtasdt0(W289_89, W393_93)))) & doDivides0(W289_89, W087_87)) | (? [W394_94] : ((aNaturalNumber0(W394_94) & =(W188_88, sdtasdt0(W289_89, W394_94)))) & doDivides0(W289_89, W188_88))))))) & (((((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)) & ? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xm), sdtasdt0(xp, W097_97))))) & doDivides0(xp, sdtasdt0(xn, xm))) & ~(? [W098_98] : ((aNaturalNumber0(W098_98) & =(sdtpldt0(xp, W098_98), xn))) | sdtlseqdt0(xp, xn)) & ~(? [W099_99] : ((aNaturalNumber0(W099_99) & =(sdtpldt0(xp, W099_99), xm))) | sdtlseqdt0(xp, xm)) & (((((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)) & ~=(xm, xp)) & ? [W0101_101] : ((aNaturalNumber0(W0101_101) & =(sdtpldt0(xm, W0101_101), xp)))) & sdtlseqdt0(xm, xp)) & ((aNaturalNumber0(xk) & =(sdtasdt0(xn, xm), sdtasdt0(xp, xk))) & =(xk, sdtsldt0(sdtasdt0(xn, xm), xp))) & ~(=(xk, sz00) | =(xk, sz10)) & (~=(xk, sz00) & ~=(xk, sz10)) & ((((((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)) & ~=(xr, sz10)) & ! [W0103_103] : (((aNaturalNumber0(W0103_103) & (? [W1104_104] : ((aNaturalNumber0(W1104_104) & =(xr, sdtasdt0(W0103_103, W1104_104)))) | doDivides0(W0103_103, xr))) => (=(W0103_103, sz10) | =(W0103_103, xr))))) & isPrime0(xr)) & ((? [W0105_105] : ((aNaturalNumber0(W0105_105) & =(sdtpldt0(xr, W0105_105), xk))) & ? [W0106_106] : ((aNaturalNumber0(W0106_106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, W0106_106))))) & doDivides0(xr, sdtasdt0(xn, xm))) & ((~=(xk, xp) & ? [W0107_107] : ((aNaturalNumber0(W0107_107) & =(sdtpldt0(xk, W0107_107), xp)))) & sdtlseqdt0(xk, xp)) & ((? [W0108_108] : ((aNaturalNumber0(W0108_108) & =(xn, sdtasdt0(xr, W0108_108)))) & doDivides0(xr, xn)) | (? [W0109_109] : ((aNaturalNumber0(W0109_109) & =(xm, sdtasdt0(xr, W0109_109)))) & doDivides0(xr, xm))) & ~(? [W0110_110] : ((aNaturalNumber0(W0110_110) & =(xn, sdtasdt0(xr, W0110_110)))) | doDivides0(xr, xn)) & ~(? [W0111_111] : ((aNaturalNumber0(W0111_111) & =(xm, sdtasdt0(xr, W0111_111)))) | doDivides0(xr, xm)) & ~(((? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))) | doDivides0(xp, xn)) | ? [W0113_113] : ((aNaturalNumber0(W0113_113) & =(xm, sdtasdt0(xp, W0113_113))))) | doDivides0(xp, xm)))
% 34.79/22.23 -> [1] ! [W05_5] : ((aNaturalNumber0(W05_5) => $true)), aNaturalNumber0(sz00), (aNaturalNumber0(sz10) & ~=(sz10, sz00)), ! [W06_6, W17_7] : (((aNaturalNumber0(W06_6) & aNaturalNumber0(W17_7)) => aNaturalNumber0(sdtpldt0(W06_6, W17_7)))), ! [W08_8, W19_9] : (((aNaturalNumber0(W08_8) & aNaturalNumber0(W19_9)) => aNaturalNumber0(sdtasdt0(W08_8, W19_9)))), ! [W010_10, W111_11] : (((aNaturalNumber0(W010_10) & aNaturalNumber0(W111_11)) => =(sdtpldt0(W010_10, W111_11), sdtpldt0(W111_11, W010_10)))), ! [W012_12, W113_13, W214_14] : ((((aNaturalNumber0(W012_12) & aNaturalNumber0(W113_13)) & aNaturalNumber0(W214_14)) => =(sdtpldt0(sdtpldt0(W012_12, W113_13), W214_14), sdtpldt0(W012_12, sdtpldt0(W113_13, W214_14))))), ! [W015_15] : ((aNaturalNumber0(W015_15) => (=(sdtpldt0(W015_15, sz00), W015_15) & =(W015_15, sdtpldt0(sz00, W015_15))))), ! [W016_16, W117_17] : (((aNaturalNumber0(W016_16) & aNaturalNumber0(W117_17)) => =(sdtasdt0(W016_16, W117_17), sdtasdt0(W117_17, W016_16)))), ! [W018_18, W119_19, W220_20] : ((((aNaturalNumber0(W018_18) & aNaturalNumber0(W119_19)) & aNaturalNumber0(W220_20)) => =(sdtasdt0(sdtasdt0(W018_18, W119_19), W220_20), sdtasdt0(W018_18, sdtasdt0(W119_19, W220_20))))), ! [W021_21] : ((aNaturalNumber0(W021_21) => (=(sdtasdt0(W021_21, sz10), W021_21) & =(W021_21, sdtasdt0(sz10, W021_21))))), ! [W022_22] : ((aNaturalNumber0(W022_22) => (=(sdtasdt0(W022_22, sz00), sz00) & =(sz00, sdtasdt0(sz00, W022_22))))), ! [W023_23, W124_24, W225_25] : ((((aNaturalNumber0(W023_23) & aNaturalNumber0(W124_24)) & aNaturalNumber0(W225_25)) => (=(sdtasdt0(W023_23, sdtpldt0(W124_24, W225_25)), sdtpldt0(sdtasdt0(W023_23, W124_24), sdtasdt0(W023_23, W225_25))) & =(sdtasdt0(sdtpldt0(W124_24, W225_25), W023_23), sdtpldt0(sdtasdt0(W124_24, W023_23), sdtasdt0(W225_25, W023_23)))))), ! [W026_26, W127_27, W228_28] : ((((aNaturalNumber0(W026_26) & aNaturalNumber0(W127_27)) & aNaturalNumber0(W228_28)) => ((=(sdtpldt0(W026_26, W127_27), sdtpldt0(W026_26, W228_28)) | =(sdtpldt0(W127_27, W026_26), sdtpldt0(W228_28, W026_26))) => =(W127_27, W228_28)))), ! [W029_29] : ((aNaturalNumber0(W029_29) => (~=(W029_29, sz00) => ! [W130_30, W231_31] : (((aNaturalNumber0(W130_30) & aNaturalNumber0(W231_31)) => ((=(sdtasdt0(W029_29, W130_30), sdtasdt0(W029_29, W231_31)) | =(sdtasdt0(W130_30, W029_29), sdtasdt0(W231_31, W029_29))) => =(W130_30, W231_31))))))), ! [W032_32, W133_33] : (((aNaturalNumber0(W032_32) & aNaturalNumber0(W133_33)) => (=(sdtpldt0(W032_32, W133_33), sz00) => (=(W032_32, sz00) & =(W133_33, sz00))))), ! [W034_34, W135_35] : (((aNaturalNumber0(W034_34) & aNaturalNumber0(W135_35)) => (=(sdtasdt0(W034_34, W135_35), sz00) => (=(W034_34, sz00) | =(W135_35, sz00))))), ! [W036_36, W137_37] : (((aNaturalNumber0(W036_36) & aNaturalNumber0(W137_37)) => (sdtlseqdt0(W036_36, W137_37) <=> ? [W238_38] : ((aNaturalNumber0(W238_38) & =(sdtpldt0(W036_36, W238_38), W137_37)))))), ! [W039_39, W140_40] : (((aNaturalNumber0(W039_39) & aNaturalNumber0(W140_40)) => (sdtlseqdt0(W039_39, W140_40) => ! [W241_41] : ((=(W241_41, sdtmndt0(W140_40, W039_39)) <=> (aNaturalNumber0(W241_41) & =(sdtpldt0(W039_39, W241_41), W140_40))))))), ! [W042_42] : ((aNaturalNumber0(W042_42) => sdtlseqdt0(W042_42, W042_42))), ! [W043_43, W144_44] : (((aNaturalNumber0(W043_43) & aNaturalNumber0(W144_44)) => ((sdtlseqdt0(W043_43, W144_44) & sdtlseqdt0(W144_44, W043_43)) => =(W043_43, W144_44)))), ! [W045_45, W146_46, W247_47] : ((((aNaturalNumber0(W045_45) & aNaturalNumber0(W146_46)) & aNaturalNumber0(W247_47)) => ((sdtlseqdt0(W045_45, W146_46) & sdtlseqdt0(W146_46, W247_47)) => sdtlseqdt0(W045_45, W247_47)))), ! [W048_48, W149_49] : (((aNaturalNumber0(W048_48) & aNaturalNumber0(W149_49)) => (sdtlseqdt0(W048_48, W149_49) | (~=(W149_49, W048_48) & sdtlseqdt0(W149_49, W048_48))))), ! [W050_50, W151_51] : (((aNaturalNumber0(W050_50) & aNaturalNumber0(W151_51)) => ((~=(W050_50, W151_51) & sdtlseqdt0(W050_50, W151_51)) => ! [W252_52] : ((aNaturalNumber0(W252_52) => (((~=(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51)) & sdtlseqdt0(sdtpldt0(W252_52, W050_50), sdtpldt0(W252_52, W151_51))) & ~=(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52))) & sdtlseqdt0(sdtpldt0(W050_50, W252_52), sdtpldt0(W151_51, W252_52)))))))), ! [W053_53, W154_54, W255_55] : ((((aNaturalNumber0(W053_53) & aNaturalNumber0(W154_54)) & aNaturalNumber0(W255_55)) => (((~=(W053_53, sz00) & ~=(W154_54, W255_55)) & sdtlseqdt0(W154_54, W255_55)) => (((~=(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55)) & sdtlseqdt0(sdtasdt0(W053_53, W154_54), sdtasdt0(W053_53, W255_55))) & ~=(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53))) & sdtlseqdt0(sdtasdt0(W154_54, W053_53), sdtasdt0(W255_55, W053_53)))))), ! [W056_56] : ((aNaturalNumber0(W056_56) => ((=(W056_56, sz00) | =(W056_56, sz10)) | (~=(sz10, W056_56) & sdtlseqdt0(sz10, W056_56))))), ! [W057_57, W158_58] : (((aNaturalNumber0(W057_57) & aNaturalNumber0(W158_58)) => (~=(W057_57, sz00) => sdtlseqdt0(W158_58, sdtasdt0(W158_58, W057_57))))), ! [W059_59, W160_60] : (((aNaturalNumber0(W059_59) & aNaturalNumber0(W160_60)) => (iLess0(W059_59, W160_60) => $true))), ! [W061_61, W162_62] : (((aNaturalNumber0(W061_61) & aNaturalNumber0(W162_62)) => ((~=(W061_61, W162_62) & sdtlseqdt0(W061_61, W162_62)) => iLess0(W061_61, W162_62)))), ! [W063_63, W164_64] : (((aNaturalNumber0(W063_63) & aNaturalNumber0(W164_64)) => (doDivides0(W063_63, W164_64) <=> ? [W265_65] : ((aNaturalNumber0(W265_65) & =(W164_64, sdtasdt0(W063_63, W265_65))))))), ! [W066_66, W167_67] : (((aNaturalNumber0(W066_66) & aNaturalNumber0(W167_67)) => ((~=(W066_66, sz00) & doDivides0(W066_66, W167_67)) => ! [W268_68] : ((=(W268_68, sdtsldt0(W167_67, W066_66)) <=> (aNaturalNumber0(W268_68) & =(W167_67, sdtasdt0(W066_66, W268_68)))))))), ! [W069_69, W170_70, W271_71] : ((((aNaturalNumber0(W069_69) & aNaturalNumber0(W170_70)) & aNaturalNumber0(W271_71)) => ((doDivides0(W069_69, W170_70) & doDivides0(W170_70, W271_71)) => doDivides0(W069_69, W271_71)))), ! [W072_72, W173_73, W274_74] : ((((aNaturalNumber0(W072_72) & aNaturalNumber0(W173_73)) & aNaturalNumber0(W274_74)) => ((doDivides0(W072_72, W173_73) & doDivides0(W072_72, W274_74)) => doDivides0(W072_72, sdtpldt0(W173_73, W274_74))))), ! [W075_75, W176_76, W277_77] : ((((aNaturalNumber0(W075_75) & aNaturalNumber0(W176_76)) & aNaturalNumber0(W277_77)) => ((doDivides0(W075_75, W176_76) & doDivides0(W075_75, sdtpldt0(W176_76, W277_77))) => doDivides0(W075_75, W277_77)))), ! [W078_78, W179_79] : (((aNaturalNumber0(W078_78) & aNaturalNumber0(W179_79)) => ((doDivides0(W078_78, W179_79) & ~=(W179_79, sz00)) => sdtlseqdt0(W078_78, W179_79)))), ! [W080_80, W181_81] : (((aNaturalNumber0(W080_80) & aNaturalNumber0(W181_81)) => ((~=(W080_80, sz00) & doDivides0(W080_80, W181_81)) => ! [W282_82] : ((aNaturalNumber0(W282_82) => =(sdtasdt0(W282_82, sdtsldt0(W181_81, W080_80)), sdtsldt0(sdtasdt0(W282_82, W181_81), W080_80))))))), ! [W083_83] : ((aNaturalNumber0(W083_83) => (isPrime0(W083_83) <=> ((~=(W083_83, sz00) & ~=(W083_83, sz10)) & ! [W184_84] : (((aNaturalNumber0(W184_84) & doDivides0(W184_84, W083_83)) => (=(W184_84, sz10) | =(W184_84, W083_83)))))))), ! [W085_85] : ((((aNaturalNumber0(W085_85) & ~=(W085_85, sz00)) & ~=(W085_85, sz10)) => ? [W186_86] : (((aNaturalNumber0(W186_86) & doDivides0(W186_86, W085_85)) & isPrime0(W186_86))))), ((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), ! [W087_87, W188_88, W289_89] : ((((aNaturalNumber0(W087_87) & aNaturalNumber0(W188_88)) & aNaturalNumber0(W289_89)) => (((((~=(W289_89, sz00) & ~=(W289_89, sz10)) & ! [W390_90] : ((((aNaturalNumber0(W390_90) & ? [W491_91] : ((aNaturalNumber0(W491_91) & =(W289_89, sdtasdt0(W390_90, W491_91))))) & doDivides0(W390_90, W289_89)) => (=(W390_90, sz10) | =(W390_90, W289_89))))) | isPrime0(W289_89)) & (? [W392_92] : ((aNaturalNumber0(W392_92) & =(sdtasdt0(W087_87, W188_88), sdtasdt0(W289_89, W392_92)))) | doDivides0(W289_89, sdtasdt0(W087_87, W188_88)))) => (iLess0(sdtpldt0(sdtpldt0(W087_87, W188_88), W289_89), sdtpldt0(sdtpldt0(xn, xm), xp)) => ((? [W393_93] : ((aNaturalNumber0(W393_93) & =(W087_87, sdtasdt0(W289_89, W393_93)))) & doDivides0(W289_89, W087_87)) | (? [W394_94] : ((aNaturalNumber0(W394_94) & =(W188_88, sdtasdt0(W289_89, W394_94)))) & doDivides0(W289_89, W188_88))))))), (((((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)) & ? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xm), sdtasdt0(xp, W097_97))))) & doDivides0(xp, sdtasdt0(xn, xm))), ~(? [W098_98] : ((aNaturalNumber0(W098_98) & =(sdtpldt0(xp, W098_98), xn))) | sdtlseqdt0(xp, xn)), ~(? [W099_99] : ((aNaturalNumber0(W099_99) & =(sdtpldt0(xp, W099_99), xm))) | sdtlseqdt0(xp, xm)), (((((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)) & ~=(xm, xp)) & ? [W0101_101] : ((aNaturalNumber0(W0101_101) & =(sdtpldt0(xm, W0101_101), xp)))) & sdtlseqdt0(xm, xp)), ((aNaturalNumber0(xk) & =(sdtasdt0(xn, xm), sdtasdt0(xp, xk))) & =(xk, sdtsldt0(sdtasdt0(xn, xm), xp))), ~(=(xk, sz00) | =(xk, sz10)), (~=(xk, sz00) & ~=(xk, sz10)), ((((((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)) & ~=(xr, sz10)) & ! [W0103_103] : (((aNaturalNumber0(W0103_103) & (? [W1104_104] : ((aNaturalNumber0(W1104_104) & =(xr, sdtasdt0(W0103_103, W1104_104)))) | doDivides0(W0103_103, xr))) => (=(W0103_103, sz10) | =(W0103_103, xr))))) & isPrime0(xr)), ((? [W0105_105] : ((aNaturalNumber0(W0105_105) & =(sdtpldt0(xr, W0105_105), xk))) & ? [W0106_106] : ((aNaturalNumber0(W0106_106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, W0106_106))))) & doDivides0(xr, sdtasdt0(xn, xm))), ((~=(xk, xp) & ? [W0107_107] : ((aNaturalNumber0(W0107_107) & =(sdtpldt0(xk, W0107_107), xp)))) & sdtlseqdt0(xk, xp)), ((? [W0108_108] : ((aNaturalNumber0(W0108_108) & =(xn, sdtasdt0(xr, W0108_108)))) & doDivides0(xr, xn)) | (? [W0109_109] : ((aNaturalNumber0(W0109_109) & =(xm, sdtasdt0(xr, W0109_109)))) & doDivides0(xr, xm))), ~(? [W0110_110] : ((aNaturalNumber0(W0110_110) & =(xn, sdtasdt0(xr, W0110_110)))) | doDivides0(xr, xn)), ~(? [W0111_111] : ((aNaturalNumber0(W0111_111) & =(xm, sdtasdt0(xr, W0111_111)))) | doDivides0(xr, xm)), ~(((? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))) | doDivides0(xp, xn)) | ? [W0113_113] : ((aNaturalNumber0(W0113_113) & =(xm, sdtasdt0(xp, W0113_113))))) | doDivides0(xp, xm))
% 34.79/22.23
% 34.79/22.23 [1] ALPHA_AND : (aNaturalNumber0(sz10) & ~=(sz10, sz00))
% 34.79/22.23 -> [2] aNaturalNumber0(sz10), ~=(sz10, sz00)
% 34.79/22.23
% 34.79/22.23 [2] ALPHA_AND : ((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp))
% 34.79/22.23 -> [3] (aNaturalNumber0(xn) & aNaturalNumber0(xm)), aNaturalNumber0(xp)
% 34.79/22.23
% 34.79/22.23 [3] ALPHA_AND : (((((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)) & ? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xm), sdtasdt0(xp, W097_97))))) & doDivides0(xp, sdtasdt0(xn, xm)))
% 34.79/22.23 -> [4] ((((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)) & ? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xm), sdtasdt0(xp, W097_97))))), doDivides0(xp, sdtasdt0(xn, xm))
% 34.79/22.23
% 34.79/22.23 [4] ALPHA_NOT_OR : ~(? [W098_98] : ((aNaturalNumber0(W098_98) & =(sdtpldt0(xp, W098_98), xn))) | sdtlseqdt0(xp, xn))
% 34.79/22.23 -> [5] ~? [W098_98] : ((aNaturalNumber0(W098_98) & =(sdtpldt0(xp, W098_98), xn))), ~sdtlseqdt0(xp, xn)
% 34.79/22.23
% 34.79/22.23 [5] ALPHA_NOT_OR : ~(? [W099_99] : ((aNaturalNumber0(W099_99) & =(sdtpldt0(xp, W099_99), xm))) | sdtlseqdt0(xp, xm))
% 34.79/22.23 -> [6] ~? [W099_99] : ((aNaturalNumber0(W099_99) & =(sdtpldt0(xp, W099_99), xm))), ~sdtlseqdt0(xp, xm)
% 34.79/22.23
% 34.79/22.23 [6] ALPHA_AND : (((((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)) & ~=(xm, xp)) & ? [W0101_101] : ((aNaturalNumber0(W0101_101) & =(sdtpldt0(xm, W0101_101), xp)))) & sdtlseqdt0(xm, xp))
% 34.79/22.23 -> [7] ((((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)) & ~=(xm, xp)) & ? [W0101_101] : ((aNaturalNumber0(W0101_101) & =(sdtpldt0(xm, W0101_101), xp)))), sdtlseqdt0(xm, xp)
% 34.79/22.23
% 34.79/22.23 [7] ALPHA_AND : ((aNaturalNumber0(xk) & =(sdtasdt0(xn, xm), sdtasdt0(xp, xk))) & =(xk, sdtsldt0(sdtasdt0(xn, xm), xp)))
% 34.79/22.23 -> [8] (aNaturalNumber0(xk) & =(sdtasdt0(xn, xm), sdtasdt0(xp, xk))), =(xk, sdtsldt0(sdtasdt0(xn, xm), xp))
% 34.79/22.23
% 34.79/22.23 [8] ALPHA_NOT_OR : ~(=(xk, sz00) | =(xk, sz10))
% 34.79/22.23 -> [9] ~=(xk, sz00), ~=(xk, sz10)
% 34.79/22.23
% 34.79/22.23 [9] ALPHA_AND : (~=(xk, sz00) & ~=(xk, sz10))
% 34.79/22.23 -> [10] ~=(xk, sz00), ~=(xk, sz10)
% 34.79/22.23
% 34.79/22.23 [10] ALPHA_AND : ((((((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)) & ~=(xr, sz10)) & ! [W0103_103] : (((aNaturalNumber0(W0103_103) & (? [W1104_104] : ((aNaturalNumber0(W1104_104) & =(xr, sdtasdt0(W0103_103, W1104_104)))) | doDivides0(W0103_103, xr))) => (=(W0103_103, sz10) | =(W0103_103, xr))))) & isPrime0(xr))
% 34.79/22.23 -> [11] (((((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)) & ~=(xr, sz10)) & ! [W0103_103] : (((aNaturalNumber0(W0103_103) & (? [W1104_104] : ((aNaturalNumber0(W1104_104) & =(xr, sdtasdt0(W0103_103, W1104_104)))) | doDivides0(W0103_103, xr))) => (=(W0103_103, sz10) | =(W0103_103, xr))))), isPrime0(xr)
% 34.79/22.23
% 34.79/22.23 [11] ALPHA_AND : ((? [W0105_105] : ((aNaturalNumber0(W0105_105) & =(sdtpldt0(xr, W0105_105), xk))) & ? [W0106_106] : ((aNaturalNumber0(W0106_106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, W0106_106))))) & doDivides0(xr, sdtasdt0(xn, xm)))
% 34.79/22.23 -> [12] (? [W0105_105] : ((aNaturalNumber0(W0105_105) & =(sdtpldt0(xr, W0105_105), xk))) & ? [W0106_106] : ((aNaturalNumber0(W0106_106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, W0106_106))))), doDivides0(xr, sdtasdt0(xn, xm))
% 34.79/22.23
% 34.79/22.23 [12] ALPHA_AND : ((~=(xk, xp) & ? [W0107_107] : ((aNaturalNumber0(W0107_107) & =(sdtpldt0(xk, W0107_107), xp)))) & sdtlseqdt0(xk, xp))
% 34.79/22.23 -> [13] (~=(xk, xp) & ? [W0107_107] : ((aNaturalNumber0(W0107_107) & =(sdtpldt0(xk, W0107_107), xp)))), sdtlseqdt0(xk, xp)
% 34.79/22.23
% 34.79/22.23 [13] ALPHA_NOT_OR : ~(? [W0110_110] : ((aNaturalNumber0(W0110_110) & =(xn, sdtasdt0(xr, W0110_110)))) | doDivides0(xr, xn))
% 34.79/22.23 -> [14] ~? [W0110_110] : ((aNaturalNumber0(W0110_110) & =(xn, sdtasdt0(xr, W0110_110)))), ~doDivides0(xr, xn)
% 34.79/22.23
% 34.79/22.23 [14] ALPHA_NOT_OR : ~(? [W0111_111] : ((aNaturalNumber0(W0111_111) & =(xm, sdtasdt0(xr, W0111_111)))) | doDivides0(xr, xm))
% 34.79/22.23 -> [15] ~? [W0111_111] : ((aNaturalNumber0(W0111_111) & =(xm, sdtasdt0(xr, W0111_111)))), ~doDivides0(xr, xm)
% 34.79/22.23
% 34.79/22.23 [15] ALPHA_NOT_OR : ~(((? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))) | doDivides0(xp, xn)) | ? [W0113_113] : ((aNaturalNumber0(W0113_113) & =(xm, sdtasdt0(xp, W0113_113))))) | doDivides0(xp, xm))
% 34.79/22.23 -> [16] ~((? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))) | doDivides0(xp, xn)) | ? [W0113_113] : ((aNaturalNumber0(W0113_113) & =(xm, sdtasdt0(xp, W0113_113))))), ~doDivides0(xp, xm)
% 34.79/22.23
% 34.79/22.23 [16] ALPHA_AND : (aNaturalNumber0(xn) & aNaturalNumber0(xm))
% 34.79/22.23 -> [17] aNaturalNumber0(xn), aNaturalNumber0(xm)
% 34.79/22.23
% 34.79/22.23 [17] ALPHA_AND : ((((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)) & ? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xm), sdtasdt0(xp, W097_97)))))
% 34.79/22.23 -> [18] (((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp)), ? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xm), sdtasdt0(xp, W097_97))))
% 34.79/22.23
% 34.79/22.23 [18] ALPHA_AND : ((((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)) & ~=(xm, xp)) & ? [W0101_101] : ((aNaturalNumber0(W0101_101) & =(sdtpldt0(xm, W0101_101), xp))))
% 34.79/22.23 -> [19] (((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)) & ~=(xm, xp)), ? [W0101_101] : ((aNaturalNumber0(W0101_101) & =(sdtpldt0(xm, W0101_101), xp)))
% 34.79/22.23
% 34.79/22.23 [19] ALPHA_AND : (aNaturalNumber0(xk) & =(sdtasdt0(xn, xm), sdtasdt0(xp, xk)))
% 34.79/22.23 -> [20] aNaturalNumber0(xk), =(sdtasdt0(xn, xm), sdtasdt0(xp, xk))
% 34.79/22.23
% 34.79/22.23 [20] ALPHA_AND : (((((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)) & ~=(xr, sz10)) & ! [W0103_103] : (((aNaturalNumber0(W0103_103) & (? [W1104_104] : ((aNaturalNumber0(W1104_104) & =(xr, sdtasdt0(W0103_103, W1104_104)))) | doDivides0(W0103_103, xr))) => (=(W0103_103, sz10) | =(W0103_103, xr)))))
% 34.79/22.23 -> [21] ((((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)) & ~=(xr, sz10)), ! [W0103_103] : (((aNaturalNumber0(W0103_103) & (? [W1104_104] : ((aNaturalNumber0(W1104_104) & =(xr, sdtasdt0(W0103_103, W1104_104)))) | doDivides0(W0103_103, xr))) => (=(W0103_103, sz10) | =(W0103_103, xr))))
% 34.79/22.23
% 34.79/22.23 [21] ALPHA_AND : (? [W0105_105] : ((aNaturalNumber0(W0105_105) & =(sdtpldt0(xr, W0105_105), xk))) & ? [W0106_106] : ((aNaturalNumber0(W0106_106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, W0106_106)))))
% 34.79/22.23 -> [22] ? [W0105_105] : ((aNaturalNumber0(W0105_105) & =(sdtpldt0(xr, W0105_105), xk))), ? [W0106_106] : ((aNaturalNumber0(W0106_106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, W0106_106))))
% 34.79/22.23
% 34.79/22.23 [22] ALPHA_AND : (~=(xk, xp) & ? [W0107_107] : ((aNaturalNumber0(W0107_107) & =(sdtpldt0(xk, W0107_107), xp))))
% 34.79/22.23 -> [23] ~=(xk, xp), ? [W0107_107] : ((aNaturalNumber0(W0107_107) & =(sdtpldt0(xk, W0107_107), xp)))
% 34.79/22.23
% 34.79/22.23 [23] ALPHA_NOT_OR : ~((? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))) | doDivides0(xp, xn)) | ? [W0113_113] : ((aNaturalNumber0(W0113_113) & =(xm, sdtasdt0(xp, W0113_113)))))
% 34.79/22.23 -> [24] ~(? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))) | doDivides0(xp, xn)), ~? [W0113_113] : ((aNaturalNumber0(W0113_113) & =(xm, sdtasdt0(xp, W0113_113))))
% 34.79/22.23
% 34.79/22.23 [24] ALPHA_AND : (((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))) & isPrime0(xp))
% 34.79/22.23 -> [25] ((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))), isPrime0(xp)
% 34.79/22.23
% 34.79/22.23 [25] ALPHA_AND : (((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)) & ~=(xm, xp))
% 34.79/22.23 -> [26] ((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp)), ~=(xm, xp)
% 34.79/22.23
% 34.79/22.23 [26] ALPHA_AND : ((((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)) & ~=(xr, sz10))
% 34.79/22.23 -> [27] (((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00)), ~=(xr, sz10)
% 34.79/22.23
% 34.79/22.23 [27] ALPHA_NOT_OR : ~(? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))) | doDivides0(xp, xn))
% 34.79/22.23 -> [28] ~? [W0112_112] : ((aNaturalNumber0(W0112_112) & =(xn, sdtasdt0(xp, W0112_112)))), ~doDivides0(xp, xn)
% 34.79/22.23
% 34.79/22.23 [28] ALPHA_AND : ((~=(xp, sz00) & ~=(xp, sz10)) & ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp)))))
% 34.79/22.23 -> [29] (~=(xp, sz00) & ~=(xp, sz10)), ! [W095_95] : (((aNaturalNumber0(W095_95) & (? [W196_96] : ((aNaturalNumber0(W196_96) & =(xp, sdtasdt0(W095_95, W196_96)))) | doDivides0(W095_95, xp))) => (=(W095_95, sz10) | =(W095_95, xp))))
% 34.79/22.23
% 34.79/22.23 [29] ALPHA_AND : ((~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))) & sdtlseqdt0(xn, xp))
% 34.79/22.23 -> [30] (~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))), sdtlseqdt0(xn, xp)
% 34.79/22.23
% 34.79/22.23 [30] ALPHA_AND : (((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)) & ~=(xr, sz00))
% 34.79/22.23 -> [31] ((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk)), ~=(xr, sz00)
% 34.79/22.23
% 34.79/22.23 [31] ALPHA_AND : (~=(xp, sz00) & ~=(xp, sz10))
% 34.79/22.23 -> [32] ~=(xp, sz00), ~=(xp, sz10)
% 34.79/22.23
% 34.79/22.23 [32] ALPHA_AND : (~=(xn, xp) & ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp))))
% 34.79/22.23 -> [33] ~=(xn, xp), ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))
% 34.79/22.23
% 34.79/22.23 [33] ALPHA_AND : ((aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))) & doDivides0(xr, xk))
% 34.79/22.23 -> [34] (aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))), doDivides0(xr, xk)
% 34.79/22.23
% 34.79/22.23 [34] ALPHA_AND : (aNaturalNumber0(xr) & ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102)))))
% 34.79/22.23 -> [35] aNaturalNumber0(xr), ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))
% 34.79/22.23
% 34.79/22.23 [35] DELTA_EXISTS : ? [W097_97] : ((aNaturalNumber0(W097_97) & =(sdtasdt0(xn, xm), sdtasdt0(xp, W097_97))))
% 34.79/22.23 -> [36] (aNaturalNumber0(skolem_W09797) & =(sdtasdt0(xn, xm), sdtasdt0(xp, skolem_W09797)))
% 34.79/22.23
% 34.79/22.23 [36] ALPHA_AND : (aNaturalNumber0(skolem_W09797) & =(sdtasdt0(xn, xm), sdtasdt0(xp, skolem_W09797)))
% 34.79/22.23 -> [37] aNaturalNumber0(skolem_W09797), =(sdtasdt0(xn, xm), sdtasdt0(xp, skolem_W09797))
% 34.79/22.23
% 34.79/22.23 [37] DELTA_EXISTS : ? [W0101_101] : ((aNaturalNumber0(W0101_101) & =(sdtpldt0(xm, W0101_101), xp)))
% 34.79/22.23 -> [38] (aNaturalNumber0(skolem_W0101101) & =(sdtpldt0(xm, skolem_W0101101), xp))
% 34.79/22.23
% 34.79/22.23 [38] ALPHA_AND : (aNaturalNumber0(skolem_W0101101) & =(sdtpldt0(xm, skolem_W0101101), xp))
% 34.79/22.23 -> [39] aNaturalNumber0(skolem_W0101101), =(sdtpldt0(xm, skolem_W0101101), xp)
% 34.79/22.23
% 34.79/22.23 [39] DELTA_EXISTS : ? [W0105_105] : ((aNaturalNumber0(W0105_105) & =(sdtpldt0(xr, W0105_105), xk)))
% 34.79/22.23 -> [40] (aNaturalNumber0(skolem_W0105105) & =(sdtpldt0(xr, skolem_W0105105), xk))
% 34.79/22.23
% 34.79/22.23 [40] ALPHA_AND : (aNaturalNumber0(skolem_W0105105) & =(sdtpldt0(xr, skolem_W0105105), xk))
% 34.79/22.23 -> [41] aNaturalNumber0(skolem_W0105105), =(sdtpldt0(xr, skolem_W0105105), xk)
% 34.79/22.23
% 34.79/22.23 [41] DELTA_EXISTS : ? [W0106_106] : ((aNaturalNumber0(W0106_106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, W0106_106))))
% 34.79/22.23 -> [42] (aNaturalNumber0(skolem_W0106106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, skolem_W0106106)))
% 34.79/22.23
% 34.79/22.23 [42] ALPHA_AND : (aNaturalNumber0(skolem_W0106106) & =(sdtasdt0(xn, xm), sdtasdt0(xr, skolem_W0106106)))
% 34.79/22.23 -> [43] aNaturalNumber0(skolem_W0106106), =(sdtasdt0(xn, xm), sdtasdt0(xr, skolem_W0106106))
% 34.79/22.23
% 34.79/22.23 [43] DELTA_EXISTS : ? [W0107_107] : ((aNaturalNumber0(W0107_107) & =(sdtpldt0(xk, W0107_107), xp)))
% 34.79/22.23 -> [44] (aNaturalNumber0(skolem_W0107107) & =(sdtpldt0(xk, skolem_W0107107), xp))
% 34.79/22.23
% 34.79/22.23 [44] ALPHA_AND : (aNaturalNumber0(skolem_W0107107) & =(sdtpldt0(xk, skolem_W0107107), xp))
% 34.79/22.23 -> [45] aNaturalNumber0(skolem_W0107107), =(sdtpldt0(xk, skolem_W0107107), xp)
% 34.79/22.23
% 34.79/22.23 [45] DELTA_EXISTS : ? [W0100_100] : ((aNaturalNumber0(W0100_100) & =(sdtpldt0(xn, W0100_100), xp)))
% 34.79/22.23 -> [46] (aNaturalNumber0(skolem_W0100100) & =(sdtpldt0(xn, skolem_W0100100), xp))
% 34.79/22.23
% 34.79/22.23 [46] ALPHA_AND : (aNaturalNumber0(skolem_W0100100) & =(sdtpldt0(xn, skolem_W0100100), xp))
% 34.79/22.23 -> [47] aNaturalNumber0(skolem_W0100100), =(sdtpldt0(xn, skolem_W0100100), xp)
% 34.79/22.23
% 34.79/22.23 [47] DELTA_EXISTS : ? [W0102_102] : ((aNaturalNumber0(W0102_102) & =(xk, sdtasdt0(xr, W0102_102))))
% 34.79/22.23 -> [48] (aNaturalNumber0(skolem_W0102102) & =(xk, sdtasdt0(xr, skolem_W0102102)))
% 34.79/22.23
% 34.79/22.23 [48] ALPHA_AND : (aNaturalNumber0(skolem_W0102102) & =(xk, sdtasdt0(xr, skolem_W0102102)))
% 34.79/22.23 -> [49] aNaturalNumber0(skolem_W0102102), =(xk, sdtasdt0(xr, skolem_W0102102))
% 34.79/22.23
% 34.79/22.23 [49] BETA_OR : ((? [W0108_108] : ((aNaturalNumber0(W0108_108) & =(xn, sdtasdt0(xr, W0108_108)))) & doDivides0(xr, xn)) | (? [W0109_109] : ((aNaturalNumber0(W0109_109) & =(xm, sdtasdt0(xr, W0109_109)))) & doDivides0(xr, xm)))
% 34.79/22.23 -> [50] (? [W0108_108] : ((aNaturalNumber0(W0108_108) & =(xn, sdtasdt0(xr, W0108_108)))) & doDivides0(xr, xn))
% 34.79/22.23 -> [51] (? [W0109_109] : ((aNaturalNumber0(W0109_109) & =(xm, sdtasdt0(xr, W0109_109)))) & doDivides0(xr, xm))
% 34.79/22.23
% 34.79/22.23 [50] ALPHA_AND : (? [W0108_108] : ((aNaturalNumber0(W0108_108) & =(xn, sdtasdt0(xr, W0108_108)))) & doDivides0(xr, xn))
% 34.79/22.23 -> [52] ? [W0108_108] : ((aNaturalNumber0(W0108_108) & =(xn, sdtasdt0(xr, W0108_108)))), doDivides0(xr, xn)
% 34.79/22.23
% 34.79/22.23 [52] CLOSURE : doDivides0(xr, xn)
% 34.79/22.23
% 34.79/22.23 [51] ALPHA_AND : (? [W0109_109] : ((aNaturalNumber0(W0109_109) & =(xm, sdtasdt0(xr, W0109_109)))) & doDivides0(xr, xm))
% 34.79/22.23 -> [53] ? [W0109_109] : ((aNaturalNumber0(W0109_109) & =(xm, sdtasdt0(xr, W0109_109)))), doDivides0(xr, xm)
% 34.79/22.23
% 34.79/22.23 [53] CLOSURE : doDivides0(xr, xm)
% 34.79/22.23
% 34.79/22.23 % SZS output end Proof for theBenchmark.p
% 34.79/22.23 [21.888764s][1][Res] 104343 goroutines created
% 34.79/22.23 ==== Result ====
% 34.79/22.23 [21.888801s][1][Res] VALID
% 34.79/22.23 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------